From ede8b62eb2393a027108823910a2c1001fb9e490 Mon Sep 17 00:00:00 2001 From: SevroAuBarca Date: Sun, 9 Oct 2022 19:48:12 -0500 Subject: [PATCH 1/6] Chapter 1 complete!! :D --- src/Chapter1.hs | 82 ++++++++++++++++++++++++++++++++----------------- 1 file changed, 53 insertions(+), 29 deletions(-) diff --git a/src/Chapter1.hs b/src/Chapter1.hs index 04fed0db..7ce371c1 100644 --- a/src/Chapter1.hs +++ b/src/Chapter1.hs @@ -4,7 +4,6 @@ Happy to see you here, on the way to the wonderful Functional Programming land with Haskell! Fight the fierce Monad Dragon and save the globe from despicable runtime exceptions! - We appreciate your curiosity and will try to provide you with all the necessary equipment for your training before the battle in the real FP world. Learning Functional Programming can be challenging. But we designed this training to be @@ -70,6 +69,7 @@ Each Haskell module starts with the "module where" line. Modules should have the same name as the corresponding file with the `.hs` extension. -} + module Chapter1 where {- | @@ -115,7 +115,7 @@ immediately see what types will be inferred. -} - {- +{- Haskell is a __compiled__ language. In the illustration below, you can see the overall picture of the process from your code to the binary of the written program: @@ -209,31 +209,31 @@ So, the output in this example means that 'False' has type 'Bool'. > Try to guess first and then compare your expectations with GHCi output >>> :t True - +True :: Bool >>> :t 'a' - +'a' :: Char >>> :t 42 - +42 :: Num p => p A pair of boolean and char: >>> :t (True, 'x') - +(True, 'x') :: (Bool, Char) Boolean negation: >>> :t not - +not :: Bool -> Bool Boolean 'and' operator: >>> :t (&&) - +(&&) :: Bool -> Bool -> Bool Addition of two numbers: >>> :t (+) - +(+) :: Num a => a -> a -> a Maximum of two values: >>> :t max - +max :: Ord a => a -> a -> a You might not understand each type at this moment, but don't worry! You've only started your Haskell journey. Types will become your friends soon. @@ -301,43 +301,43 @@ expressions in GHCi functions and operators first. Remember this from the previous task? ;) >>> 1 + 2 - +3 >>> 10 - 15 - +-5 >>> 10 - (-5) -- negative constants require () - +15 >>> (3 + 5) < 10 - +True >>> True && False - +False >>> 10 < 20 || 20 < 5 - +True >>> 2 ^ 10 -- power - +1024 >>> not False - +True >>> div 20 3 -- integral division - +6 >>> mod 20 3 -- integral division remainder - +2 >>> max 4 10 - +10 >>> min 5 (max 1 2) - +2 >>> max (min 1 10) (min 5 7) - +5 Because Haskell is a __statically-typed__ language, you see an error each time you try to mix values of different types in situations where you are not @@ -429,6 +429,7 @@ task is to specify the type of this function. 49 -} +squareSum :: Int -> Int -> Int squareSum x y = (x + y) * (x + y) @@ -448,8 +449,9 @@ Implement the function that takes an integer value and returns the next 'Int'. every type ｑ.β˜†.*ｑ. No need to worry much about "error" here, just replace the function body with the proper implementation. -} + next :: Int -> Int -next x = error "next: not implemented!" +next x = x + 1 {- | After you've implemented the function (or even during the implementation), you @@ -490,7 +492,9 @@ Implement a function that returns the last digit of a given number. whether it works for you! -} -- DON'T FORGET TO SPECIFY THE TYPE IN HERE -lastDigit n = error "lastDigit: Not implemented!" + +lastDigit :: Int -> Int +lastDigit n = mod n 10 {- | @@ -519,8 +523,9 @@ branches because it is an expression and it must always return some value. πŸ‘©β€πŸ”¬ Due to lazy evaluation in Haskell, only the expression from the branch satisfying the check will be returned and, therefore, evaluated. -} + closestToZero :: Int -> Int -> Int -closestToZero x y = error "closestToZero: not implemented!" +closestToZero x y = if abs y > abs x then x else y {- | @@ -554,7 +559,11 @@ value after "=" where the condition is true. Casual reminder about adding top-level type signatures for all functions :) -} -mid x y z = error "mid: not implemented!" +mid :: Int -> Int -> Int -> Int +mid x y z + | (x > y && x < z) || (x < y && x > z) = x + | (y > x && y < z) || (y < x && y > z) = y + | (z > y && z < x) || (z < y && z > x) = z {- | =βš”οΈ= Task 8 @@ -568,8 +577,15 @@ True >>> isVowel 'x' False -} -isVowel c = error "isVowel: not implemented!" +isVowel :: Char -> Bool +isVowel c + | c == 'a' = True + | c == 'e' = True + | c == 'i' = True + | c == 'o' = True + | c == 'u' = True + | otherwise = False {- | == Local variables and functions @@ -631,8 +647,16 @@ Implement a function that returns the sum of the last two digits of a number. Try to introduce variables in this task (either with let-in or where) to avoid specifying complex expressions. -} +sumLast2 :: Int -> Int +sumLast2 n = modDigits n + where + modDigits :: Int -> Int + modDigits x + | x < 10 = x + | x < 100 = mod x 10 + | x < 1000 = mod x 100 + | otherwise = mod x 1000 -sumLast2 n = error "sumLast2: Not implemented!" {- | From 2bec970d057a2a4455e2f739a91ceff6226b8037 Mon Sep 17 00:00:00 2001 From: SevroAuBarca Date: Wed, 12 Oct 2022 21:45:19 -0500 Subject: [PATCH 2/6] Chapter 2 complete --- src/Chapter1.hs | 6 ++-- src/Chapter2.hs | 89 ++++++++++++++++++++++++++++++++++++------------- 2 files changed, 68 insertions(+), 27 deletions(-) diff --git a/src/Chapter1.hs b/src/Chapter1.hs index 7ce371c1..85867d6f 100644 --- a/src/Chapter1.hs +++ b/src/Chapter1.hs @@ -494,7 +494,7 @@ Implement a function that returns the last digit of a given number. -- DON'T FORGET TO SPECIFY THE TYPE IN HERE lastDigit :: Int -> Int -lastDigit n = mod n 10 +lastDigit n = mod (abs n) 10 {- | @@ -563,7 +563,7 @@ mid :: Int -> Int -> Int -> Int mid x y z | (x > y && x < z) || (x < y && x > z) = x | (y > x && y < z) || (y < x && y > z) = y - | (z > y && z < x) || (z < y && z > x) = z + | otherwise = z {- | =βš”οΈ= Task 8 @@ -677,8 +677,6 @@ You need to use recursion in this task. Feel free to return to it later, if you aren't ready for this boss yet! -} -firstDigit n = error "firstDigit: Not implemented!" - {- You did it! Now it is time to open a pull request with your changes diff --git a/src/Chapter2.hs b/src/Chapter2.hs index f7c02ce2..1dcc99d7 100644 --- a/src/Chapter2.hs +++ b/src/Chapter2.hs @@ -136,43 +136,43 @@ functions in GHCi and insert the corresponding resulting output below: List of booleans: >>> :t [True, False] - +[True, False] :: [Bool] String is a list of characters: >>> :t "some string" - +"some string" :: [Char] Empty list: >>> :t [] - +[] :: [a] Append two lists: >>> :t (++) - +(++) :: [a] -> [a] -> [a] Prepend an element at the beginning of a list: >>> :t (:) - +(:) :: a -> [a] -> [a] Reverse a list: >>> :t reverse - +reverse :: [a] -> [a] Take first N elements of a list: >>> :t take - +take :: Int -> [a] -> [a] Create a list from N same elements: >>> :t replicate - +replicate :: Int -> a -> [a] Split a string by line breaks: >>> :t lines - +lines :: String -> [String] Join a list of strings with line breaks: >>> :t unlines - +unlines :: [String] -> String -} @@ -186,30 +186,43 @@ Evaluate the following expressions in GHCi and insert the answers. Try to guess first, what you will see. >>> [10, 2] ++ [3, 1, 5] +[10,2,3,1,5] >>> [] ++ [1, 4] -- [] is an empty list +[1,4] >>> 3 : [1, 2] +[3, 1, 2] >>> 4 : 2 : [5, 10] -- prepend multiple elements +[4,2,5,10] >>> [1 .. 10] -- list ranges +[1,2,3,4,5,6,7,8,9,10] >>> [10 .. 1] +[] >>> [10, 9 .. 1] -- backwards list with explicit step +[10,9,8,7,6,5,4,3,2,1] >>> length [4, 10, 5] -- list length +3 >>> replicate 5 True +[True,True,True,True,True] >>> take 5 "Hello, World!" +"Hello" >>> drop 5 "Hello, World!" +", World!" >>> zip "abc" [1, 2, 3] -- convert two lists to a single list of pairs +[('a',1),('b',2),('c',3)] >>> words "Hello Haskell World!" -- split the string into the list of words +["Hello","Haskell","World!"] @@ -335,8 +348,14 @@ from it! ghci> :l src/Chapter2.hs -} +import Data.List + subList :: Int -> Int -> [a] -> [a] -subList = error "subList: Not implemented!" +subList num1 num2 arr + | num1 == num2 = take 1 (drop num1 arr) + | num1 < num2 = take (num2 - num1 + 1) (drop num1 arr) + | num1 < 0 || num2 < 0 = [] + | otherwise = [] {- | =βš”οΈ= Task 4 @@ -349,7 +368,10 @@ Implement a function that returns only the first half of a given list. "b" -} -- PUT THE FUNCTION TYPE IN HERE -firstHalf l = error "firstHalf: Not implemented!" +firstHalf :: [a] -> [a] +firstHalf l + | null l == True = [] + | null l == False = take (div (length l) 2) l {- | @@ -501,8 +523,9 @@ True >>> isThird42 [42, 42, 0, 42] False -} -isThird42 = error "isThird42: Not implemented!" - +isThird42 :: [Int] -> Bool +isThird42 (_ : _ : 42 : _)= True +isThird42 _ = False {- | =πŸ›‘= Recursion @@ -605,8 +628,10 @@ Implement a function that duplicates each element of the list "aabbaacc" -} + duplicate :: [a] -> [a] -duplicate = error "duplicate: Not implemented!" +duplicate [] = [] +duplicate (x:xs) = x : x : duplicate xs {- | @@ -621,7 +646,15 @@ Write a function that takes elements of a list only in even positions. >>> takeEven [2, 1, 3, 5, 4] [2,3,4] -} -takeEven = error "takeEven: Not implemented!" + +takeEven :: [a] -> [a] +takeEven arr = go 1 arr + where + go :: Int -> [a] -> [a] + go acc [] = [] + go acc (x:xs) + | mod acc 2 /= 0 = x : go (acc + 1) xs + | otherwise = go (acc + 1) xs {- | =πŸ›‘= Higher-order functions @@ -727,8 +760,9 @@ value of the element itself πŸ•― HINT: Use combination of 'map' and 'replicate' -} + smartReplicate :: [Int] -> [Int] -smartReplicate l = error "smartReplicate: Not implemented!" +smartReplicate l = concatMap (\x -> replicate x x) l {- | =βš”οΈ= Task 9 @@ -741,7 +775,8 @@ the list with only those lists that contain a passed element. πŸ•― HINT: Use the 'elem' function to check whether an element belongs to a list -} -contains = error "contains: Not implemented!" +contains :: Int -> [[Int]] -> [[Int]] +contains x array = filter (\val -> elem x val ) array {- | @@ -780,14 +815,15 @@ nextInt = add 1 Let's now try to eta-reduce some of the functions and ensure that we mastered the skill of eta-reducing. -} + divideTenBy :: Int -> Int -divideTenBy x = div 10 x +divideTenBy = div 10 -- TODO: type ;) -listElementsLessThan x l = filter (< x) l +listElementsLessThan x = filter (< x) -- Can you eta-reduce this one??? -pairMul xs ys = zipWith (*) xs ys +pairMul xs = zipWith (*) xs {- | =πŸ›‘= Lazy evaluation @@ -842,7 +878,12 @@ list. πŸ•― HINT: Use the 'cycle' function -} -rotate = error "rotate: Not implemented!" +rotate :: Int -> [a] -> [a] +rotate x [] = [] +rotate x arr + | x < 0 = [] + | x == 0 = arr + | otherwise = take (length arr) (drop x (cycle arr)) {- | =πŸ’£= Task 12* @@ -858,7 +899,9 @@ and reverses it. function, but in this task, you need to implement it manually. No cheating! -} -rewind = error "rewind: Not Implemented!" +rewind :: [a] -> [a] +rewind [] = [] +rewind (x:s) = rewind s ++ [x] {- From d07205b2f2f3dfb604f97eafc63911a9ea1bd26a Mon Sep 17 00:00:00 2001 From: SevroAuBarca Date: Wed, 12 Oct 2022 21:53:34 -0500 Subject: [PATCH 3/6] Chapter 2 complete --- src/Chapter1.hs | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Chapter1.hs b/src/Chapter1.hs index 85867d6f..41917de5 100644 --- a/src/Chapter1.hs +++ b/src/Chapter1.hs @@ -677,7 +677,7 @@ You need to use recursion in this task. Feel free to return to it later, if you aren't ready for this boss yet! -} - +firstDigit n = error "firstDigit: Not implemented!" {- You did it! Now it is time to open a pull request with your changes and summon @vrom911 and @chshersh for the review! From ac2781e5e68c8aa10ec291f6527088e3f71b0028 Mon Sep 17 00:00:00 2001 From: SevroAuBarca Date: Wed, 12 Oct 2022 22:00:42 -0500 Subject: [PATCH 4/6] Chapter 2 complete --- src/Chapter1.hs | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Chapter1.hs b/src/Chapter1.hs index 41917de5..94a88abc 100644 --- a/src/Chapter1.hs +++ b/src/Chapter1.hs @@ -676,7 +676,7 @@ Implement a function that returns the first digit of a given number. You need to use recursion in this task. Feel free to return to it later, if you aren't ready for this boss yet! -} - +firstDigit :: Int -> Int firstDigit n = error "firstDigit: Not implemented!" {- You did it! Now it is time to open a pull request with your changes From d9e8f4ad8f8326b148f3cb88fe207e1e0397291e Mon Sep 17 00:00:00 2001 From: SevroAuBarca Date: Wed, 12 Oct 2022 22:07:33 -0500 Subject: [PATCH 5/6] Chapter 2 complete --- src/Chapter2.hs | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Chapter2.hs b/src/Chapter2.hs index 1dcc99d7..3ee6911f 100644 --- a/src/Chapter2.hs +++ b/src/Chapter2.hs @@ -823,7 +823,7 @@ divideTenBy = div 10 listElementsLessThan x = filter (< x) -- Can you eta-reduce this one??? -pairMul xs = zipWith (*) xs +pairMul x = zipWith (*) x {- | =πŸ›‘= Lazy evaluation From 437dae55395904d13822beb7e3a6ed1628e03c47 Mon Sep 17 00:00:00 2001 From: SevroAuBarca Date: Wed, 12 Oct 2022 22:24:12 -0500 Subject: [PATCH 6/6] Chapter 1 Complete again --- src/Chapter1.hs | 1 + src/Chapter2.hs | 268 +++--------------------------------------------- 2 files changed, 14 insertions(+), 255 deletions(-) diff --git a/src/Chapter1.hs b/src/Chapter1.hs index 94a88abc..9b404e32 100644 --- a/src/Chapter1.hs +++ b/src/Chapter1.hs @@ -647,6 +647,7 @@ Implement a function that returns the sum of the last two digits of a number. Try to introduce variables in this task (either with let-in or where) to avoid specifying complex expressions. -} + sumLast2 :: Int -> Int sumLast2 n = modDigits n where diff --git a/src/Chapter2.hs b/src/Chapter2.hs index 3ee6911f..4473ffd7 100644 --- a/src/Chapter2.hs +++ b/src/Chapter2.hs @@ -1,21 +1,14 @@ {- πŸ‘‹ Welcome to Chapter Two, Traveller! - If you haven't finished Chapter One yet, we encourage you to check it out, as the knowledge from the previous section is required in order to pass this training. - If you already finished Chapter One β€” congratulations and huge respect! We are happy to see you with us at the next step. - A casual reminder of how it works. - == You are on __Chapter Two__. - Here we will explore more interesting functional concepts. We are going to practice our skills on the list type in Haskell. - In this chapter, you are going to master: - ✧ The list data type ✧ Immutability ✧ Pattern-matching @@ -25,16 +18,13 @@ In this chapter, you are going to master: ✧ Higher-order functions ✧ Partial function application ✧ Eta-reduction - As usual, the explanations are in the Haskell comments of this module. We are leaving a number of tasks on our path. Your goal is to solve them all and make the tests for Chapter Two green. - After finishing the PR, you can choose to summon us, @vrom911 and @chshersh, to look at your solution in order to give some advice on your code. This is optional; however, you can ask us for review only if you want some feedback on your solutions. - Now, if you are ready, bring it on! -} @@ -42,49 +32,38 @@ module Chapter2 where {- =πŸ›‘= Imports - Before we start diving into the FP concepts, let's cover an important process-development detail. - Without any additional effort, in Haskell you have access to all functions defined in the special module called "Prelude". This module is always imported by default and contains all primitive data types and useful functions to work with them. However, sometimes you need to import other modules even from other libraries. - The Haskell Standard library is called "base". It provides modules to work with different data types and values. If you want to bring some additional types and functions in scope, you need to import them manually. - For example, to import the list sorting function, you need to write: - @ import Data.List (sort) @ - All imports should go at the beginning of the module: after the "module MODULE_NAME where" line and before the first function (or type) definition. - β™« NOTE: you can use Hoogle to explore modules and functions from other places as well. - When working with lists, the most practical module will be "Data.List": - * https://hackage.haskell.org/package/base-4.14.0.0/docs/Data-List.html -} {- | =πŸ›‘= Lists - __List__ is a crucial data type in Haskell and functional programming in general. It represents a collection of elements of the _same type_. The list type is written as the type of list element in square brackets. For example, a list of integers will have type '[Int]' and a list of booleans β€” '[Bool]'. - [Interesting fact]: String in Haskell is a list of characters ('Char' data type in Haskell) and is written as '[Char]'. But Haskell also provides the "String" alias to '[Char]'. So, in some places, you will @@ -92,7 +71,6 @@ see 'String', and in others, you will see '[Char]', but they mean the same thing. We will explain better how it works in Chapter Three. For now, you only need to know that you can use 'String' and '[Char]' interchangeably. - To create a list, you need to put elements in square brackets (the same as used for the list type) and separate them by commas. Such expressions are called __list literals__. For example, the expression @@ -100,29 +78,24 @@ expressions are called __list literals__. For example, the expression element is number 3, and the last element is number 1. Similarly, you can create a list of two booleans: [False, True]. A list without elements is just []. - You probably noticed that lists could be of any type of elements. Often you want to write a function that works with lists of any type (but consistent inside one list). This feature is called __parametric polymorphism__. It will be explained in more detail later, but when working with lists, you often will see type signatures like: - @ foo :: [a] -> [b] -> [a] @ - The above type signature means that this function takes two lists: one with elements of some type "a" and another with elements of type "b" (the function doesn't care about the specific types) and returns the list with elements of the same type as the first list. Such words "a" and "b" are called __type variables__. - For comparison, specific types in Haskell start with an uppercase letter (Int, Bool, Char, etc.), where type variables begin with a lowercase letter (a, b, el, etc.). This is the way to distinguish between these types. - The Haskell standard library already provides a lot of functions to work with lists. And you will need to operate a lot with standard functions in the upcoming exercises. Remember, Hoogle is your friend! @@ -130,111 +103,56 @@ functions in the upcoming exercises. Remember, Hoogle is your friend! {- | =βš”οΈ= Task 1 - Explore lists by checking types of various list expressions and functions in GHCi and insert the corresponding resulting output below: - List of booleans: >>> :t [True, False] -[True, False] :: [Bool] - String is a list of characters: >>> :t "some string" -"some string" :: [Char] - Empty list: >>> :t [] -[] :: [a] - Append two lists: >>> :t (++) -(++) :: [a] -> [a] -> [a] - Prepend an element at the beginning of a list: >>> :t (:) -(:) :: a -> [a] -> [a] - Reverse a list: >>> :t reverse -reverse :: [a] -> [a] - Take first N elements of a list: >>> :t take -take :: Int -> [a] -> [a] - Create a list from N same elements: >>> :t replicate -replicate :: Int -> a -> [a] - Split a string by line breaks: >>> :t lines -lines :: String -> [String] - Join a list of strings with line breaks: >>> :t unlines -unlines :: [String] -> String - -} {- | =βš”οΈ= Task 2 - To understand the list type better, it is also beneficial to play with list expressions in REPL. - Evaluate the following expressions in GHCi and insert the answers. Try to guess first, what you will see. - >>> [10, 2] ++ [3, 1, 5] -[10,2,3,1,5] - >>> [] ++ [1, 4] -- [] is an empty list -[1,4] - >>> 3 : [1, 2] -[3, 1, 2] - >>> 4 : 2 : [5, 10] -- prepend multiple elements -[4,2,5,10] - >>> [1 .. 10] -- list ranges -[1,2,3,4,5,6,7,8,9,10] - >>> [10 .. 1] -[] - >>> [10, 9 .. 1] -- backwards list with explicit step -[10,9,8,7,6,5,4,3,2,1] - >>> length [4, 10, 5] -- list length -3 - >>> replicate 5 True -[True,True,True,True,True] - >>> take 5 "Hello, World!" -"Hello" - >>> drop 5 "Hello, World!" -", World!" - >>> zip "abc" [1, 2, 3] -- convert two lists to a single list of pairs -[('a',1),('b',2),('c',3)] - >>> words "Hello Haskell World!" -- split the string into the list of words -["Hello","Haskell","World!"] - - - πŸ‘©β€πŸ”¬ Haskell has a lot of syntax sugar. In the case with lists, any list literal like "[3, 1, 2]" is syntax sugar for prepending elements at the empty list: "3 : 1 : 2 : []". - Don't forget that lists are the containers of the same-type elements. Meaning, you can't combine lists of different types in any situation. Let's try appending a list of booleans and a string (list of characters) to see the error message: - ghci> [True, False] ++ "string" :4:18: error: β€’ Couldn't match type β€˜Char’ with β€˜Bool’ @@ -243,25 +161,20 @@ ghci> [True, False] ++ "string" β€’ In the second argument of β€˜(++)’, namely β€˜"string"’ In the expression: [True, False] ++ "string" In an equation for β€˜it’: it = [True, False] ++ "string" - -} {- | =πŸ›‘= Immutability - At this point in our training, you need to learn that all values in Haskell are immutable! Woohoo! But what does it mean for us? - It means that when you apply a function to some variable, the value is not changed. Instead, you create a new value each time. - >>> import Data.List (sort) -- sort is not in Prelude >>> x = [3, 1, 2] -- you can assign values to variables in GHCi >>> sort x [1,2,3] >>> x [3,1,2] - The 'sort' function returns a new sorted list. It doesn't change the original list, so you don't need to worry about accidentally spoiling values of variables you defined before. @@ -269,7 +182,6 @@ values of variables you defined before. {- | =πŸ›‘= List implementation - Let's talk a bit about list implementation details. Lists in Haskell are implemented as __linked lists__ (or cons-lists). And because everything in Haskell is immutable, adding elements at the beginning @@ -277,147 +189,108 @@ of the lists is cheap. Haskell doesn't need to allocate new memory and copy the whole list there; it can just create a new list from a new element and a pointer to an already existing list. In other words, tails of lists are shared. - For these reasons, adding elements to and extracting elements from the beginning of a list is much cheaper and faster than working with the end of the list. - In some sense, lists are similar to trains. Let's look at an illustration of a two-element list: - . . . . . o o o o o _________ _________ ____ o | y | | x | |[]\_n][. _|________|_o_|________|_o_|__|____)< oo oo oo oo oo 00-oo\_ - y : x : [] - You can see that adding new elements (railway carriages) to the left is easy: you just need to connect them to the last element in the chain. - . . . . . o o o o o _________ _________ _________ ____ o | z | | y | | x | |[]\_n][. _|________|_o_|________|_o_|________|_o_|__|____)< oo oo oo oo oo oo oo 00-oo\_ - z : y : x : [] - But imagine how much difficult it would be to add new carriages to the right? - . . . . . o o o o o _________ _________ _________ ____ o | y | | x | | z | |[]\_n][. _|________|_o_|________|_o_|________|_o_|__|____)< oo oo oo oo oo oo oo 00-oo\_ - y : x : z : [] - You can't simply attach a new carriage anymore. You need to detach the locomotive, maybe move trains around the railway a bit for the proper position, and only then attach everything back again. The same thing with adding elements to the end of the list β€” it is a slow and costly process. - -} {- | =βš”οΈ= Task 3 - Let's write our first function to process lists in Haskell! Your first implementation task is to write a function that returns all elements of a list between two given positions inclusive (starting from zero). - Remember that each function returns a new list. - >>> subList 3 5 [1 .. 10] [4,5,6] >>> subList 3 0 [True, False, False, True, False] [] - β™« NOTE: When implementing, think about various corner cases. You should return an empty list when given numbers that are negative. - And also don't forget to check the 'Data.List' module. It is full of yummy functions. - Don't forget that you can load this module in GHCi to call functions from it! - ghci> :l src/Chapter2.hs -} -import Data.List - subList :: Int -> Int -> [a] -> [a] -subList num1 num2 arr - | num1 == num2 = take 1 (drop num1 arr) - | num1 < num2 = take (num2 - num1 + 1) (drop num1 arr) - | num1 < 0 || num2 < 0 = [] - | otherwise = [] +subList = error "subList: Not implemented!" {- | =βš”οΈ= Task 4 - Implement a function that returns only the first half of a given list. - >>> firstHalf [3, 4, 1, 2] [3,4] >>> firstHalf "bca" "b" -} -- PUT THE FUNCTION TYPE IN HERE -firstHalf :: [a] -> [a] -firstHalf l - | null l == True = [] - | null l == False = take (div (length l) 2) l +firstHalf l = error "firstHalf: Not implemented!" {- | =πŸ›‘= Pattern matching - One of the coolest and most powerful features of Functional Programming is __pattern matching__. This feature allows you to match on different values of a type and produce results based on patterns. The syntax of using pattern matching is similar to defining ordinary functions, but instead of using variable names, you use the values. - For example, the "not" function that returns "the other" boolean is implemented like this: - @ not :: Bool -> Bool not True = False not False = True @ - To perform pattern-matching, repeat a function name as many times as many patterns you want to cover. The cool thing about Haskell is that the compiler warns you if you forget to cover some cases. So you always can be sure that your patterns are exhaustive! - Note that you can pattern match on a variable too! Variable is like a pattern that matches any value and gives it a name. You can think of variables in function definitions as special cases of pattern matching. - You can pattern match on numbers as well! For example, if you want to write a function that checks whether the given number is zero, you can write it in the following way: - @ isZero :: Int -> Bool isZero 0 = True isZero n = False @ - Instead of "isZero n = False" you can write "isZero _ = False". The symbol "_" (underscore) is called __hole__, and it is used when we don't care about the value of a variable. It is like a pattern that always matches (the same as a variable), but we don't use its value. - πŸ‘©β€πŸ”¬ Unlike 'switch' and 'case' in other languages, that try to go through each switch and perform all actions in there until it reaches the breakpoint, pattern matching on function parameters in Haskell @@ -428,8 +301,6 @@ always matches (the same as a variable), but we don't use its value. thing to keep in mind, especially when you have overlapping patterns. Also note that, if no pattern matches the value, the function fails at runtime. - - In addition to pattern matching in the function definition, you can also use the __case-of__ expression. With case-of, you specify the patterns to match and expressions to return depending on a pattern @@ -437,10 +308,8 @@ inside the function body. The main difference between 'case-of' and top-level pattern matching is the fact that 'case' uses arrows (->) instead of "=" for branch results. The "case" is often helpful when function names are long, or pattern-matching on functions is awkward. - To understand case-of, let's look at a function that takes two numbers and a symbol, representing a math operation on these symbols. - @ evalOperation :: Char -> Int -> Int -> Int evalOperation op x y = case op of @@ -450,61 +319,49 @@ evalOperation op x y = case op of '/' -> div x y _ -> 0 @ - β™« NOTE: Each branch with a pattern should have the same alignment! Remember that Haskell is a _layout-sensitive_ language. Also, note that in the last line, "_" goes directly under the single quote to have the same indentation πŸ”. You can try copying the function and change the indentation to see the parser error (which is not that clever to identify the indentation errors). - Since we are talking about lists in this chapter, let's see how we can use pattern-matching on them! It turns out, pattern matching on lists is an effective and inevitable technique. - We can pattern-match on list literals directly: - @ isEmpty :: [a] -> Bool isEmpty [] = True isEmpty _ = False - sumThree :: [Int] -> Int sumThree [x, y, z] = x + y + z sumThree _ = 0 - onlyTwoElements :: [a] -> Bool onlyTwoElements [_, _] = True onlyTwoElements _ = False @ - Remember the ":" operator to add elements at the beginning of a list? Turns out, in case of lists this operator can be used for pattern matching as well! Isn't this cool? For example: - @ -- return the first element of the list or default if the list is empty headOrDef :: a -> [a] -> a headOrDef def [] = def headOrDef _ (x:_) = x - -- check if the first list element is zero firstIsZero :: [Int] -> Bool firstIsZero (0:_) = True firstIsZero _ = False - -- check that a list has at least two elements atLeastTwo :: [a] -> Bool atLeastTwo (_ : _ : _) = True atLeastTwo _ = False @ - When matching on the ":" pattern, the first element of the list goes to the left side of ':' and the tail of the list goes to the right side. You can have even nested patterns (as in the last example above). In other words, when writing a pattern like "(x:y:xs)", it is the same as writing "(x:(y:xs))". - β™« NOTE: Often, pattern matching can be replaced with conditional checks (if-then-else, guards) and vice versa. In some cases pattern-matching can be more efficient; in other cases, it can produce @@ -514,51 +371,40 @@ the same as writing "(x:(y:xs))". {- | =βš”οΈ= Task 5 - Implement a function that checks whether the third element of a list is the number 42. - >>> isThird42 [1, 2, 42, 10] True >>> isThird42 [42, 42, 0, 42] False -} -isThird42 :: [Int] -> Bool -isThird42 (_ : _ : 42 : _)= True -isThird42 _ = False +isThird42 = error "isThird42: Not implemented!" + {- | =πŸ›‘= Recursion - Often, when writing in a functional style, you end up implementing __recursive__ functions. Recursive functions are nothing more than calling the function itself from the body of the same function. - Of course, you need some stopping conditions to exit the function eventually, and you need to think carefully whether your function ever reaches the stop condition. However, having pattern-matching in our arsenal of skills significantly increases our chances of writing correct functions. Nevertheless, you should think mindfully on how your recursive function behaves on different corner-cases. - A simple recursive function can divide a number by 2 until it reaches zero: - @ divToZero :: Int -> Int divToZero 0 = 0 divToZero n = divToZero (div n 2) @ - But as you can see, the function is not that helpful per se. Often you implement a helper function with some accumulator in order to collect some information during recursive calls. - For example, we can patch the previous function to count the number of steps we need to take in order to reduce the number to zero. - πŸ€” Blitz question: can you guess what this number represents? - @ divToZero :: Int -> Int divToZero n = go 0 n @@ -567,49 +413,37 @@ divToZero n = go 0 n go acc 0 = acc go acc n = go (acc + 1) (div n 2) @ - πŸ‘©β€πŸ”¬ The pattern of having a recursive helper function is called "Recursive go": - * https://kowainik.github.io/posts/haskell-mini-patterns#recursive-go - One of the most useful capabilities of pattern matching on lists is the ability to implement recursive functions with them as well! - β™« NOTE: The canonical naming scheme for such patterns is `(x:xs)` where x is the first element of the list, and xs β€” rest of the list (which is a list as well that even could be empty). - @ -- list length len :: [a] -> Int len [] = 0 len (_:xs) = 1 + len xs - -- add 10 to every number of a list addEvery10 :: [Int] -> [Int] addEvery10 [] = [] addEvery10 (x:xs) = (x + 10) : addEvery10 xs @ - When writing such functions, we usually handle two cases: empty list and non-empty list (list with at least one element in the beginning) and we decide what to do in each case. - Most of the time, the case with a non-empty list uses the recursive call to the function itself. - An example of a standard Haskell function is 'concat' that takes a list of lists and returns a flat list, appending all intermediate lists: - @ concat :: [[a]] -> [a] concat [] = [] concat (x:xs) = x ++ concat xs @ - And it works like this: - >>> concat [[2, 1, 3], [1, 2, 3, 4], [0, 5]] [2,1,3,1,2,3,4,0,5] -} @@ -617,80 +451,55 @@ And it works like this: {- | =βš”οΈ= Task 6 - Implement a function that duplicates each element of the list - πŸ•― HINT: Use recursion and pattern matching on the list. - >>> duplicate [3, 1, 2] [3,3,1,1,2,2] >>> duplicate "abac" "aabbaacc" - -} - duplicate :: [a] -> [a] -duplicate [] = [] -duplicate (x:xs) = x : x : duplicate xs +duplicate = error "duplicate: Not implemented!" {- | =βš”οΈ= Task 7 Write a function that takes elements of a list only in even positions. - πŸ•― HINT: You need to write a recursive function that pattern matches on the list structure. Your function will have several cases and probably needs to use nested pattern matching on lists of size at least 2. Alternatively, you can use the "Recursive go" pattern. - >>> takeEven [2, 1, 3, 5, 4] [2,3,4] -} - -takeEven :: [a] -> [a] -takeEven arr = go 1 arr - where - go :: Int -> [a] -> [a] - go acc [] = [] - go acc (x:xs) - | mod acc 2 /= 0 = x : go (acc + 1) xs - | otherwise = go (acc + 1) xs +takeEven = error "takeEven: Not implemented!" {- | =πŸ›‘= Higher-order functions - Some functions can take other functions as arguments. Such functions are called __higher-order functions__ (HOFs). Check the types of some common HOF list functions: - >>> :t filter filter :: (a -> Bool) -> [a] -> [a] >>> :t map map :: (a -> b) -> [a] -> [b] - And few usage examples of those functions: - >>> filter even [1..10] -- keep only even elements in the list [2,4,6,8,10] >>> map not [True, False, True] -- maps the 'not' function over each element of the given list [False,True,False] - Having HOFs in your language means that functions can be treated in the same way as any other values and expressions: - ✲ You can pass functions as arguments ✲ You can return functions as results ✲ You can compose functions easily to create new functions ✲ You can have lists of functions ✲ And much more! - The ability to create __lambdas__ (or anonymous functions) nicely complements the concept of HOF. For example, we can easily add number 3 to each element of the list by introducing a lambda function: - >>> map (\x -> x + 3) [0..5] [3,4,5,6,7,8] - The syntax of lambda functions is somewhat similar to normal ones, except for you don't need to think about its name, which is awesome. To establish the start of the lambda function, you should @@ -698,15 +507,12 @@ write "\" which is a bit similar to the lambda symbol β€” Ξ». Then you specify space-separated arguments. Instead of the "=" in the ordinary function body, you should write "->" and then you can use these arguments and all variables in scope inside the lambda-body. - These are equal: - @ foo a b = a + b --and \a b -> a + b @ - What's even cooler is the ability to __apply functions partially__ This means that you can provide only some arguments to a function and treat the result as a function itself! You already know the 'div' @@ -716,94 +522,70 @@ partially, we will get a new function that takes only one number and returns the result of dividing 10 by that number. You can check the difference by inspecting the types of corresponding expressions in GHCi: - >>> :t +d div div :: Integer -> Integer -> Integer >>> :t +d div 10 div 10 :: Integer -> Integer - - This fact can be used to pass partial applications of some functions directly to other functions. - >>> map (div 10) [1 .. 10] [10,5,3,2,2,1,1,1,1,1] - You can apply operators partially too! - >>> filter (< 3) [2, 1, 3, 4, 0, 5] [2,1,0] >>> map (* 2) [1..5] [2,4,6,8,10] - The implementation of the "map" function is pretty straightforward if you are already familiar with function application, recursion and pattern matching. - @ map :: (a -> b) -> [a] -> [b] map _ [] = [] map f (x:xs) = f x : map f xs @ - Now you can see that there is nothing magic in HOFs in the end! -} {- | =βš”οΈ= Task 8 - Implement a function that repeats each element as many times as the value of the element itself - >>> smartReplicate [3, 1, 2] [3,3,3,1,2,2] - πŸ•― HINT: Use combination of 'map' and 'replicate' -} - smartReplicate :: [Int] -> [Int] -smartReplicate l = concatMap (\x -> replicate x x) l +smartReplicate l = error "smartReplicate: Not implemented!" {- | =βš”οΈ= Task 9 - Implement a function that takes a number, a list of lists and returns the list with only those lists that contain a passed element. - >>> contains 3 [[1, 2, 3, 4, 5], [2, 0], [3, 4]] [[1,2,3,4,5],[3,4]] - πŸ•― HINT: Use the 'elem' function to check whether an element belongs to a list -} -contains :: Int -> [[Int]] -> [[Int]] -contains x array = filter (\val -> elem x val ) array +contains = error "contains: Not implemented!" {- | =πŸ›‘= Eta-reduction - Another consequence of the HOFs and partial application is __eta-reduction__. This term is used to call the simplification of functions over their arguments. Specifically, if we have `foo x = bar 10 x`, this precisely means that `foo` is a partially applied `bar 10`. And we can write it like `foo = bar 10`. - This concept can be used to write functions as well. - For example, - @ nextInt :: Int -> Int nextInt n = add 1 n @ - Could be written with the eta-reduced form: - @ nextInt :: Int -> Int nextInt = add 1 @ - β™« NOTE: See that the initial type of the function is not changed and it works absolutely the same. We just can skip the last argument and amend its usage in the function body. @@ -811,47 +593,38 @@ nextInt = add 1 {- | =βš”οΈ= Task 10 - Let's now try to eta-reduce some of the functions and ensure that we mastered the skill of eta-reducing. -} - divideTenBy :: Int -> Int -divideTenBy = div 10 +divideTenBy x = div 10 x -- TODO: type ;) -listElementsLessThan x = filter (< x) +listElementsLessThan x l = filter (< x) l -- Can you eta-reduce this one??? -pairMul x = zipWith (*) x +pairMul xs ys = zipWith (*) xs ys {- | =πŸ›‘= Lazy evaluation - Another unique Haskell feature is __lazy evaluation__. Haskell is lazy by default, which means that it doesn't evaluate expressions when not needed. The lazy evaluation has many benefits: avoid doing redundant work, provide more composable interfaces. And in this section, we will focus on Haskell's ability to create infinite data structures and work with them! - For instance, the Haskell standard library has the 'repeat' function that returns an infinite list created from a given element. Of course, we can't print an infinite list to our terminal; it will take an infinite amount of time! But we can work with parts of it due to lazy evaluation: - >>> take 5 (repeat 0) [0,0,0,0,0] - Another useful construction is an infinite list of all numbers! - >>> take 4 [0 ..] [0,1,2,3] - Isn't this awesome?! Now we can unleash the real power of the Infinity Stone! - β™« NOTE: Infinite lists bring great power, but with great power comes great responsibility. Functions like 'length' hang when called on infinite lists. So make sure you think about such corner cases in the @@ -861,47 +634,32 @@ Infinity Stone! {- | =βš”οΈ= Task 11 - Rotating a list by a single element is the process of moving the first element of the list to the end. - Implement a function to rotate a given finite list by N elements. Try to do it more efficiently than rotating by a single element N times. - On invalid input (negative rotation coefficient) it should return an empty list. - >>> rotate 1 [1,2,3,4] [2,3,4,1] >>> rotate 3 [1,2,3,4] [4,1,2,3] - πŸ•― HINT: Use the 'cycle' function -} -rotate :: Int -> [a] -> [a] -rotate x [] = [] -rotate x arr - | x < 0 = [] - | x == 0 = arr - | otherwise = take (length arr) (drop x (cycle arr)) +rotate = error "rotate: Not implemented!" {- | =πŸ’£= Task 12* - Now you should be ready for the final boss at the end of this chapter! To defeat the boss, implement the reversing function that takes a list and reverses it. - >>> rewind [1 .. 5] [5,4,3,2,1] - β™« NOTE: The Haskell standard library already provides the "reverse" function, but in this task, you need to implement it manually. No cheating! -} -rewind :: [a] -> [a] -rewind [] = [] -rewind (x:s) = rewind s ++ [x] +rewind = error "rewind: Not Implemented!" {-